Control Charts
"The purpose [of control charts] is, [Deming] emphasizes, 'to stop people from chasing down causes.' Properly understood, a control chart is a continuing guide to constant improvement…
Writes Dr. Deming on this subject, "The production worker requires only a knowledge of simple arithmetic to plot a chart. But he cannot by himself decide that he will use a chart on the job, and still less can he start a movement for use of charts.
"It is the responsibility of management to teach the use of control charts on the job [ongoing] where they can be effective… Proliferation of charts without purpose is to be avoided."
- Walton, Mary. The Deming Management Method. (p. 113)
Dr. Shewhart invented a new way to think about uniformity and non-uniformity. He saw two kinds of variation — variation from common causes and variation from special causes. Common causes of variation produce points on a control chart that over a long period of time fall inside the control limits. Common causes of variation stay the same day-to-day, lot-to-lot. A special cause of variation is something special, not part of the system of common causes. It is detected by a point that falls outside the control limits…
A point outside the control limits is a signal (an operational definition for action) of special cause (called by Dr. Shewhart an assignable cause) which indicates the need for action— try to identify the special cause, and if it can recur, eliminate it. If all the points fall within the control limits for a long period, assume that the variation is random, common cause only, no special cause present.
- Deming, Dr. W.E. The New Economics, 3rd ed. (pp. 120-121)
IN TODAY’S POST we will look at a defining tool of the Deming management method, the Statistical Process Control Chart, aka Shewhart Chart, and more recently known as the Process Behaviour Chart. It is a deceptively simple visual aid for interpreting the state of a system or process as either stable and predictable or unstable and unpredictable.
History
Dr. Walter Shewhart is credited with first publishing in 1924 the results of research he was doing into product uniformity and consistency issues in telephones for Bell Labs at the Hawthorne Plant of Western Electric Ltd. in Chicago. Like most marketing campaigns of the time and since, their advertising slogan, “As alike as two telephones”, was proving difficult to sustain in reality. Dr. Shewhart was assigned to find out why there seemed to be no satisfactory way to start or stop the production line on the basis of isolated samples: He either stopped a perfectly good run of telephones, or let defective ones through.
Through a series of experiments, he came to realize there are two types of unavoidable mistakes made in management, which will be made in varying proportions from time to time.
Mistake 1: To react to an outcome as if it came from a special cause, when actually it came from common-causes of variation.
Mistake 2: To treat an outcome as if it came from common causes of variation, when actually it came from a special cause.
- Deming, Dr. W.E. The New Economics, 3rd ed. (p. 68)
These mistakes can be costly, so Dr. Shewhart focused his energies on researching techniques for minimizing the economic loss from either (as they could not be avoided entirely), with the outcome being the “Control Chart” or “Shewhart Chart”.
Pictured below is a Shewhart Chart from Dr. Shewhart’s book, Statistical Method from the Viewpoint of Quality Control where he plotted observations on the speed of light, which has no “true” value, but is dependent on the methods used for observation:
Basic Anatomy of a Control Chart
A Statistical Process Control Chart (or Process Behaviour Chart) is a standard 2-dimensional time-series/run-chart that is tracking a set of measurements or counts with a few added enhancements to aid in speedy interpretation of results:
Process performance data points, usually in blue with circular markers;
Control Line (CL) calculated as the mean of the tracked data points, usually identified as a solid green line.
An Upper Process Limit (UPL) line, calculated at three sigma units above the Control Line - usually identified as a solid red line;
A Lower Process Limit (LPL) line, calculated at three sigma units below the Control Line, which, depending on the nature of the data and context may default to zero, as shown in the chart below. It is also identified as a solid red line.
Why 3σ Limits?
In the original Shewhart Charts, the upper and lower limits were calculated as three standard deviations from the mean, which, when you are analyzing mechanically-drawn samples (as Dr. Deming demonstrates in the Red Bead Experiment) is appropriate because the statistical frame can be known. However, when we are looking for evidence of special causes in a process (an analytical study), estimates of 3σ units are more appropriate.
As Dr. Donald Wheeler explains in Understanding Statistical Process Control:
A “sigma unit” is a measure of scale for the data… By shifting from measurement units into sigma units, it is possible to characterize how much of the data will be within a given distance on either side of the average. Thus, sigma units express the number of measurement units that correspond to one standard unit of dispersion. (p. 61)
In his original research, Dr. Shewhart chose three sigma process limits as the most effective for finding true signals of special causes based on empirical observations of many datasets. Dr. Wheeler concurs, also noting that they are designed to be a form of “brute force” - anything that gets past this “filter” is exceeding the prior patterns of common causes in the data and can be considered a signal extraordinary variation.
The Voice of the Process vs. The Voice of the Customer
New users of control charts may confuse the calculated upper and lower process limits with specification limits and so draw idealized ones on the chart to indicate where the data points should fall between. Dr. Deming warns against this mistake: “If you use specification limits as control limits, you’ll be tampering, making things worse.”
Why? Because the limits are arbitrary to what the process is actually capable of doing, and when data points cross these drawn-in limits, you will be making Mistake 1, with reactions driving ever more variation into the process.
For clarity, consider the process limits on a control chart as the voice of the process, and specification limits as the voice of the customer. Act on signals in the former to improve the process so as to achieve the latter.
Using
In The New Economics, Dr. Deming advises on how to use a control chart with a simple process flow, shown below. He was of the strong opinion that while control charts are easy to produce and well within the reach of workers to do so, the responsibility for learning, teaching, and applying them resided with management because of the underlying aim: To improve quality by improving processes. As Dr. Deming notes in The New Economics:
Once statistical control is achieved (no indication over a long period of time of the existence of a special cause), the next step is improvement of the process, provided the economic advantage hoped for will be a good investment, in view of the expected cost of improvement. Improvement may be defined as:
1. Narrower variation.
2. Move the average to the optimum level.
3. Both.(p. 122)
Analyzing
As noted in the quoted excerpts above, the original intent of a control chart is to provide a quick and easy way to spot potential special causes of variation so as to avoid over or under reacting to changes in a process’ performance over time. A data point above the upper process limit or below the lower process limit is a strong signal of special causes and is worth investigating. If a process has many points going above or below, it is said to be unstable and unpredictable.
Weaker signals of special causes are also possible to see in the data that is within the control limits, as Mark Graban notes in his recent book on creating and using control charts, Measures of Success:
Rule 2 signals are defined as having eight or more consecutive data points above or below the Control Line (mean), while Rule 3 signals have three out of four consecutive data points closer to a process limit than the Control Line.
False Signals
Control charts are not infallible - it is possible for apparent signals to be inconclusive, or the absence of a signal to remain hidden in the data, as the weaker rules for special causes can suggest. Again, the aim of seeing process performance data in a control chart is to know whether it is in statistical control and thus predictable into the future.
Important Application: Managing People
In their book, Understanding Statistical Process Control, Dr. Donald Wheeler and David Chambers note:
The objective of the control chart is insight into the process, not practice in arithmetic. If the control chart already shows some out-of-control points, the proper course of action is to look for the Assignable Causes of these out-of-control values. (p. 226)
Dr. Deming would concur and go further, that the ultimate reason to look for assignable causes of variation is for the appropriate management of people in a system toward the improvement of quality. Invariably, control charts prompt tracing special causes upstream for system-wide effects that are causing instability downstream. This is the real power behind visualizing system data on a control chart: As an empirical aid to guide improvement.
Reflection Questions
How could plotting your own system’s data on a run-chart aid your understanding of what types of variation they present and the mistakes that are made in reaction to changes in the data? What type of mistake do your or your leadership bias toward? How would a control chart change understanding and leadership behaviours?